9x^2-46x^2+5=0

Solution for 9x^2-46x^2+5=0 equation:

9x^2-46x^2+5=0

We add all the numbers together, and all the variables

-37x^2+5=0

a = -37; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-37)·5
Δ = 740
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{185}}{2*-37}=\frac{0-2\sqrt{185}}{-74}
=-\frac{2\sqrt{185}}{-74}
=-\frac{\sqrt{185}}{-37}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{185}}{2*-37}=\frac{0+2\sqrt{185}}{-74}
=\frac{2\sqrt{185}}{-74}
=\frac{\sqrt{185}}{-37}
$